Proceed through the next round of shafts and corridors, after a while you'll finally reach a Save station - the last one in the game. Save your game, then jump up through the hole in the ceiling. In the next room, jump up out of the sticky water substance and you'll find yourself in a massive cavern. Way, way up the top of the cavern you'll find three different openings in the roof.
The one on the right leads to an energy refill ball and a Missile refill pod, so definitely head up there. The center opening leads to an Ice Beam, make sure you pick this one up, it'll be critical, you'll see why soon.
Once you're ready, head up the opening on the left. When you enter the shaft the music will become much more tense and mysterious, so we're nearly home. Climb up the shaft, then scale the next one. Use the Spider Ball to enter the narrow tunnel above the shaft, in this room you'll see in plain sight the Metroid hatchling's egg waiting to be discovered - but you won't be able to reach it yet. As you go forward below the egg Samus will freeze and the music will go crazy. The Metroid counter will then go berserk and change from 1 to 9, so there's more Metroids to face before confronting the Queen.
Drop down into the next corridor and head right. Watch out as a normal Metroid will fly straight at you in an attempt to cling to Samus, if it catches you go back up to the previous room to get rid of it. Freeze the Metroid with the Ice Beam and hammer away at it with Missiles. In the next shaft another Metroid is waiting, finish it off and climb up the shaft. Two more Metroids await in the next shaft, blast them and move onward. Another two await in the next corridor, the final two reside in the next shaft leading down. Once you've blasted them all it's finally time to face the Metroid Queen.
Enter the next corridor and the music will become deep and booming, indicating that you're nearly there. Cross the corridor, then once you reach a spike-filled section, Space Jump over the spikes and drop down through the hole in the corner.
You'll drop into the Metroid Queen's room on the right side, while the Queen resides on the left. It'll be absolutely massive, but it'll stay on the left most of the time. The Queen will often lash its head out and extend its neck to charge at Samus, this move will be difficult to dodge as the head will lash around the room. Once the Queen retracts its head, it'll spit out three large spiked balls.
They'll scatter about and fly at Samus, try to jump up as they go past. You'll need to hit the Queen in the face with well more than 100 missiles, so you'll need full energy to survive. If you manage to hit the inside of the Queen's mouth when it opens, the Queen will freeze and stop moving for a few seconds. This'll give you plenty of time to unload a barrage of missiles into the mouth, just try to keep hitting the inside of the mouth.
If you're low on health and need to escape, activate the Morphing Ball and crawl through the small tunnel below the Queen to land in the room below containing the Ice Beam, from here you can reload your missiles and fill up on health before trying again. The Screw Attack also comes in handy when the spiked balls bounce around the room. Keep pounding the Queen's head with Missiles and try not to waste too many shots, eventually the Queen will begin to disintegrate while an earthquake occurs.
Alternate method:
Thanks to Lightning Bug for pointing this trick out to me. Try to freeze the Queen's head while it's open right in front of Samus, lined up with the ground. Then activate the Morph Ball and roll into the mouth while it's open. If you've done it right, you'll get stuck in the head as the Queen retracts its neck. From here you'll be able to lay countless bombs to damage the Queen, but hold left and you'll crawl into its stomach.
Lay a bomb and it'll spit you out after taking a pounding from the bomb, after a few bombs in the belly you'll give the Queen a permanent stomach ache and it'll disintegrate. You'll take damage while inside the Queen, but it'll be pittens compared to her normal attacks. Try it out!
Your health will somehow be fully restored and the Metroid counter will finally reach zero. Once the Queen disappears, go left to find the all-important Metroid hatchling. The hatchling will break out of its egg and cling to Samus, thinking she's its mother. It's now time to leave. Head right through the caverns and shafts, whenever you find blocks obstructing the path the hatchling will break through them for you - a nice friendly gesture from the little fella.
Keep going through the tunnels and eventually you'll emerge back out onto the surface of the planet. Go right and Space Jump up the massive wall you'll find there. Scale over the top of the terrain above, then drop down the cliff to find Samus' ship. Jump inside it to complete the game. Mission complete.
Phew, the marathon's over. If you've played through the game for the first time, you'll probably beat it in about 4-6 hours, but with practice you should easily gain success in under three hours to claim the best ending the game has to offer.
This game's very different from the other Metroids as it's more like a progressive maze, but the enjoyment's still there in full.
Now that you've beaten Metroid II, it's on to the Ceres Space Colony in Super Metroid to discover the fate of Samus and the Metroid hatchling!